Question

An economist wants to determine the relationship between a person's age (in years) and his or her annual income in thousands of dollars). After gathering data from a sample of adults and fitting a regression model, the economist gets the following output from Excel: 0.523 0.274 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.244 49.637 27 ANOVA df F Significance F 0.005 9.412 Regression Residual Total 1 25 26 SS MS 23190.436 23190.436 61596.524 2463.861 84786.96 Intercept age Coefficients -12.667 2.930 Standard Error 41.162 0.955 t Stat -0.308 3.068 P-value 0.761 0.005 Lower 95% Upper 95% -97.441 72.107 0.963 4.897 Use the output above to answer the following questions by filling in the blanks below. Be sure to follow any special directions for entering your answer. Remember, age is measured in years, and income is measured in thousands of dollars. a). Use the output to write out the estimated model. Round all numbers to three (3) decimal places. A age b). Interpret the 95% confidence interval for the regression slope in the context of the problem by filling in the template below. Round all numbers to three (3) decimal places. The economist can be 95% confident that the increase in mean for a one- increase in is between $ thousand and $ thousand. C). The estimated mean annual income for a person who is 35 years old schooling would be $ thousand. Round your answer to three (3) decimal places. d). The percentage of variability in income that is explained by the model using "age" is Enter your answer as a percentage to one (1) decimal place.

Answer 1

a) Income = 12.667 + 2.93*age

b) The economist can be 95% confident that the increase in mean income for a one-unit increase in age is between $0.963 and $4.897 thousand.

c) The estimated mean annual income for a person who is 35 years old schooling would be $115.217 thousand

d) The percentage of variability that is explained by the model using "age" is 27.4.